Dyson's "win or bust" attempt to grab a Ryder Cup place saw him charge into the early first-round lead at the final qualifying event but bogeys at two of his last three holes, the seventh and ninth, saw him complete his first round at four under on 68.
Finch, however, was the early clubhouse leader two shots better off after a bogey-free round and three birdies in his final five holes.
While Dyson was initially all smiles, he has raced to six under par after 14 holes, compatriot Ross McGowan's dream of a debut appeared to have been wrecked by a return of shoulder trouble.
Needing a top-two finish just to have a chance, McGowan slumped to five over par.
Earlier this year he suffered knee and then wrist problems, but it is the trapped nerve which has now derailed his bid in the final move of the 12-month race.
The 28-year-old, excused the eve-of-tournament pro-am on medical grounds, managed only four pitch shots on the practice range yesterday before calling a halt.
Despite pain-killers and strapping he dropped shots on the 10th, 13th, 15th and long 16th, where he was in a greenside bunker for two, left it in and then missed from seven feet.
Even when he struck his tee shot to 15 feet on the 194-yard next he squatted down in clear pain and then got up feeling his shoulder and chest.
Playing partner Miguel Angel Jimenez had every sympathy, but the injury was good news for the 46-year-old Spaniard, currently in the hot seat of ninth on the points table.
Pushed down into the last automatic qualifying spot by Peter Hanson's Czech Open win on Sunday, Jimenez made a late decision to play rather than take the week off.
That meant missing his nephew's wedding - unless he misses the cut tomorrow night - but the Dubai Desert Classic and French Open champion was off to a good start and stood two under after 15 holes.
Should Dyson win on Sunday, however, Jimenez would have to finish in the top nine to keep him at bay.
His countryman Alvaro Quiros was in the same position as Dyson entering the week - nothing less than victory would suffice - but he finished his first round on level par.